5. (a) Referring to figure 2(a), calculate the numerical aperture of the human eye assuming the pupil has a diameter of 8mm and the refractive index of the vitreous humour is 1.338. [5 marks]
(b) If the pupil of the eye is opened only to a diameter of 3mm, calculate the minimum angular separation between two green pixels (520nm wavelength) which can be resolved at diffraction limit of the eye. [5 marks]
(c) (i) Using the modulation transfer function of the human eye with 3 mm pupil opening (Fig 2(b)), calculate the minimum resolvable separation between two pixels on a screen which is placed 7cm from the eye and using the criterion that at least 20% contrast is required to resolve two pixels. [5 marks]
(ii) A computer display has a screen resolution of 2048x1536 in a screen area of 196mm by 149mm. Is this display at the resolution limit of human eye which can focus at it from a distance of 7cm? [5 marks]
(d) There are 2.2 million green cones in the fovea centralis (which is a circular area with diameter of 0.3mm). Using the result calculated in (b) for diffraction limited performance (i.e. pupil has an opening of 3mm), state the minimum spacing of cones required to avoid spatial aliasing in the fovea centralis for green light (520nm wavelength). Calculate the average spacing between green cones. Is this sufficient to avoid spatial aliasing? [5 marks]
Iris Pupil Cornea
Posterior chamber Anterior chamber filled with aqueous humor
Zonular fibers Ciliary muscle
Retina Lens
Vitreous humor
Choroid 23mm
Sclera
Optic disc
Optic nerve Fovea
1 Group A (20-30 years old)
0.8
3 mm
MTF 0.6 4 mm
6 mm
0.4
0.2
0 0 10 20 30 40 50 60
Spatial Frequency (Cycles/degree)
Figure 2 (a) Diagram of human eye; (b) MTF of human eye at different pupil diameter.